Image forming apparatus

ABSTRACT

An image forming apparatus of this invention determines a correction amount for each image signal so as to correct banding as periodic density unevenness in a sub scanning direction, corrects each pixel value of an n-bit image signal in accordance with the correction amount, generates the first corrected image signal, and quantizes, for each pixel, the first corrected image signal into a second corrected image signal of m bits smaller than n bits. This image forming apparatus diffuses, in a main scanning direction, quantization errors at the time of quantization of the first corrected image signal into the second corrected image signal so as to cancel the quantization errors within a predetermined region including a plurality of continuous pixels on a main scanning line.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an image forming apparatus such as acopying machine or printer which uses an electrophotographic system orelectrostatic recording system.

2. Description of the Related Art

In an image forming apparatus of the electrophotographic system, densityunevenness (known as banding) occurs in the sub scanning direction of animage due to the periodic rotation unevenness of a photosensitive drum,intermediate transfer belt driving roller, development roller itself,motors and gears which drive them, or the like. More specifically, asrotation unevenness occurs in a photosensitive drum, the laser writeposition periodically varies. In addition, when rotation unevennessoccurs in the driving roller of the intermediate transfer belt, thetransfer position periodically varies. Furthermore, when rotationunevenness occurs in the development roller, the development stateperiodically varies. Variations in position lead to variations inscanning line interval (so-called pitch errors), which appear as densityunevenness. In addition, variations in development are variations inmain scanning line density, and appear as density unevenness. Theseperiodic variations appear as banding on an image, resulting in adeterioration in print quality.

To solve this problem of banding, Japanese Patent Laid-Open No.2007-108246 has proposed a technique of correcting an image signal so asto cancel banding, that is, a so-called banding image correction method.

Conceivable banding image correction methods include a densitycorrection method of correcting the tones of an image in oppositedirections so as to cancel density unevenness caused by the aboveposition offsets and variations in development state and a positioncorrection method of moving scanning positions on an image signal inopposite directions so as to cancel the above position offsets. Aconceivable position correction method is a method of performing pseudocorrection for less than one line by using multilevel values for PWM(Pulse Width Modulation) in addition to line-based correction.

Japanese Patent Laid-Open No. 2007-108246 has proposed a method ofsolving density unevenness in the sub scanning direction by the abovedensity correction. More specifically, first of all, a density sensormeasures the density unevenness of banding caused by an image formingapparatus. This method then predicts density unevenness during imageformation from the measured density unevenness, and corrects an imagesignal so as to cancel the density unevenness. When, for example,density correction is performed before halftone processing, thecorrected state may not be stored depending on the subsequent halftoneprocessing, resulting in a failure to reduce banding. In addition,performing the above position correction will make the above problemmore noticeable. It is therefore necessary to perform banding imagecorrection after halftone processing. On the other hand, in order toreduce the amount of data transferred, save memory, and reduce the costof a PWM circuit, the number of bits of an image signal after halftoneprocessing is preferably smaller than that before halftone processing.

If, however, the number of bits of an image signal is small, since theresolution is not high enough to reflect a correction amount, thecorrection accuracy becomes insufficient. This rather worsens the imagequality. For example, horizontal streaks appear due to correctionerrors. FIG. 24 shows examples of pitch errors as correction resultsobtained when the above position correction is performed for bandingcaused by pitch errors of a given period after halftone processing, andthe resultant correction amounts are quantized into 8-bit data each and4-bit data each. Obviously, the 8-bit quantization (solid line) for theoriginal pitch errors (thick line) suppresses the pitch errors to almost0, whereas the 4-bit quantization (broken line) produce sudden largepitch errors, which cause a deterioration in image quality in the formof sudden streaks. That is, the smaller the number of bits expressing acorrection amount, the larger a quantization error.

SUMMARY OF THE INVENTION

One aspect of the present invention provides an image forming apparatuscomprising: a correction amount determination unit which determines acorrection amount for an image signal so as to correct banding asperiodic density unevenness in a sub scanning direction; an imagecorrection unit which corrects each pixel value of an n-bit image signalin accordance with the correction amount determined by the correctionamount determination unit and outputs the image signal as a firstcorrected image signal; and a quantization unit which quantizes, foreach pixel, the first corrected image signal corrected by the imagecorrection unit into a second corrected image signal of m bits smallerthan n bits, wherein the quantization unit diffuses, in a main scanningdirection, quantization errors at the time of quantization of the firstcorrected image signal into the second corrected image signal so as tocancel the quantization errors within a predetermined region including aplurality of continuous pixels on a main scanning line.

Another aspect of the present invention provides an image formingapparatus comprising: a correction amount determination unit whichdetermines a correction amount for an image signal so as to correctbanding as periodic density unevenness in a sub scanning direction; aquantization unit which quantizes the correction amount determined bythe correction amount determination unit from n bits to m bits smallerthan the n bits; a conversion unit which converts the correction amountquantized by the quantization unit into a modified correction amountindicating a correction amount for each block including a plurality ofcontinuous pixels in a main scanning direction; and an image correctionunit which corrects the image signal by adding a block-based modifiedcorrection amount converted by the conversion unit to a pixel of anm-bit image signal which corresponds to the block, wherein theconversion unit performs conversion such that an average value ofblock-based modified correction amounts becomes nearest to a correctionamount.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments (with reference to theattached drawings).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of an image forming apparatus;

FIG. 2 shows the arrangement of a density sensor;

FIGS. 3A to 3E show the arrangement of a motor;

FIG. 4 shows signal processing units;

FIG. 5 shows sensor signals;

FIG. 6 shows the overall arrangement of a system;

FIG. 7 is a flowchart for the creation of an output correction table;

FIG. 8 is a timing chart showing how an FG signal is reset;

FIG. 9 shows how a test patch is exposed and detected;

FIG. 10 shows an exposure timing;

FIGS. 11A to 11C show correction tables;

FIG. 12 is a graph showing correction table interpolation;

FIG. 13 is a timing chart showing the relationship between FG countervalue and exposure timing at the time of image formation;

FIG. 14 is a flowchart showing an image correction process in the firstand second embodiments;

FIG. 15 is a flowchart showing a correction amount modification processin the first embodiment;

FIG. 16 is a flowchart showing synchronization between image data and FGpulses;

FIG. 17 shows quantized values;

FIG. 18 shows density correction and correction amount modification;

FIGS. 19A and 19B are flowcharts showing another correction amountmodification process;

FIG. 20 is a view showing another correction amount modification;

FIG. 21 is a view showing other correction tables;

FIG. 22 is a flowchart showing another image correction;

FIG. 23 is a view showing another image correction; and

FIG. 24 is a view showing a problem in a comparative example.

DESCRIPTION OF THE EMBODIMENTS

Embodiments of the present invention will now be described in detailwith reference to the drawings. It should be noted that the relativearrangement of the components, the numerical expressions and numericalvalues set forth in these embodiments do not limit the scope of thepresent invention unless it is specifically stated otherwise.

First Embodiment Arrangement of Image Forming Apparatus

An example of the arrangement of an image forming apparatus according tothe present invention will be described first with reference FIG. 1.First of all, this image forming apparatus forms an electrostatic latentimage by exposure light emitted based on the image information suppliedfrom an image processing unit, and forms a single-color toner image bydeveloping the electrostatic latent image. The apparatus then formssingle-color toner images of the respective colors, superimposes them,and transfers them onto a printing medium P. The apparatus fixes themulticolor toner image on the printing medium P, and delivers it outsidethe apparatus. This operation will be described in detail below.

First of all, the printing medium P is fed from a paper feed unit 21 aor 21 b. Photosensitive drums (image carriers) 22, i.e., 22Y, 22M, 22C,and 22K, are formed by coating the outer surface of aluminum cylinderswith organic photoconductive layers, which rotate upon reception ofdriving force from driving motors 6 a to 6 d (not shown). Injectionchargers 23, i.e., 23Y, 23M, 23C, and 23K, charge the photosensitivedrums 22. The four injection chargers 23Y, 23M, 23C, and 23Krespectively correspond to yellow (Y), magenta (M), cyan (C), and black(K). Each injection charger 23 includes a sleeve indicated by thecircular section. Scanner units 24Y, 24M, 24C, and 24K output exposurelight. Selectively exposing the surfaces of the photosensitive drums22Y, 22M, 22C, and 22K to light will form electrostatic latent images.Note that the photosensitive drums 22Y to 22K each rotate with apredetermined decentering component. At the time of the formation ofelectrostatic latent images, however, the phase relationship between therespective photosensitive drums 22 has already been adjusted to exertthe same decentering influence on the transfer unit. Developing devices26, i.e., 26Y, 26M, 26C, and 26K, form developer images by developingthe electrostatic images using the developers supplied from tonercartridges 25Y, 25M, 25C, and 25K. The four developing devices 26Y, 26M,26C, and 26K respectively correspond to yellow (Y), magenta (M), cyan(C), and black (K). The respective developing devices are provided withsleeves 26YS, 26MS, 26CS, and 26KS. In addition, the respectivedeveloping devices are detachably mounted in the image formingapparatus.

An intermediate transfer member 27 is in contact with the photosensitivedrums 22Y, 22M, 22C, and 22K. A driving roller 52 of the intermediatetransfer member rotates the intermediate transfer member 27 clockwise atthe time of image formation. As the photosensitive drums 22Y, 22M, 22C,and 22K rotate, the respective toner images are superimposed andtransferred onto the intermediate transfer member 27. A transfer roller28 then comes into contact with the intermediate transfer member 27 toconvey the printing medium P while clamping it between them.Consequently, the multicolor toner image on the intermediate transfermember 27 is transferred onto the printing medium P. The transfer roller28 abuts against the printing medium P at a position 28 a whiletransferring the multicolor toner image onto the printing medium P.After the transfer processing, the transfer roller 28 moves away fromthe printing medium P to a position 28 b.

A fixing device 30 fuses and fixes the transferred multicolor tonerimage while conveying the printing medium P. As shown in FIG. 1, thefixing device 30 includes a fixing roller 31 which heats the printingmedium P and a pressure roller 32 for pressing the printing medium Pagainst the fixing roller 31. The fixing roller 31 and the pressureroller 32 are formed into hollow shapes, and respectively incorporateheaters 33 and 34. That is, the fixing roller 31 and the pressure roller32 convey the printing medium P holding the multicolor toner image, andfix the toner on the surface of the printing medium P by heating andpressing it.

A delivery roller delivers the printing medium P, after the toner imageis fixed, onto a delivery tray. The apparatus then terminates the imageforming operation. A cleaning unit 29 cleans the toner remaining on theintermediate transfer member 27. The waste toner after the transfer ofthe multicolor toner image of four colors formed on the intermediatetransfer member 27 onto the printing medium P is stored in a clearercontainer. A density sensor 51 is placed in the image forming apparatusin FIG. 1 so as to face the intermediate transfer member 27. The densitysensor 51 measures the density of each toner patch formed on the surfaceof the intermediate transfer member 27 and outputs a density detectionsignal.

Although this embodiment will exemplify an image forming apparatusincluding the intermediate transfer member 27, the present invention canalso be applied to an image forming apparatus using the primary transfersystem designed to directly transfer the toner images (developer images)developed on the photosensitive drums 22 onto a printing medium. In thiscase, replacing the intermediate transfer member 27 with a printingmedium convey belt (printing medium carrier) can practice the presentinvention. Referring to the sectional view shown in FIG. 1, eachphotosensitive drum 22 is provided with a motor 6 as a driving unit.However, the plurality of photosensitive drums 22 may share the motor 6.In the following description, in contrast to the main scanning directionof an image, for example, a direction perpendicular to the main scanningdirection when viewed from above, for example, the conveying directionof a printing medium or the rotating direction of the intermediatetransfer member will be referred to as a conveying direction or a subscanning direction.

<Arrangement of Density Sensor 51>

An example of the density sensor 51 such as an optical characteristicdetection sensor will be described next with reference to FIG. 2. Asindicated by 2 a in FIG. 2, the density sensor 51 includes an LED 8 as alight-emitting element and a phototransistor 10 as a light-receivingelement. The light emitted from the LED 8 passes through a slit 9 forsuppressing diffused light, and reaches the surface of the intermediatetransfer member 27. The phototransistor 10 receives the specular lightcomponent after an opening portion 11 suppresses the irregularlyreflected light.

In FIG. 2, 2 b shows the circuit arrangement of the density sensor 51. Aregister 12 divides a voltage to the phototransistor 10 and Vcc. Aresistor 13 limits the current which drives the LED 8. A transistor 14turns off the LED 8 in accordance with a signal from a CPU 401. In thecircuit shown in 2 b in FIG. 2, the larger the amount of specular lightfrom a toner image upon irradiation with light from the LED 8, thelarger a current flowing in the phototransistor 10, and the larger thevalue of a voltage V1 detected as “OutPut”. In other words, in thearrangement shown in 2 b in FIG. 2, when the density of a patch is highand the amount of specular light is large, the detected voltage V1 ishigh, and vice versa.

<Arrangement of Motor 6>

The arrangement of the motor as a banding source to be corrected will bedescribed next with reference to FIGS. 3A to 3E. The general arrangementof the motor 6 will be described first with reference to FIGS. 3A to 3D.The mechanism of periodic rotation unevenness occurring in the motor 6will be described with reference to FIG. 3E. The following willexemplify the motor as a rotation member as a banding source. However, abanding source is not limited to this. For example, a belt drivingroller, photosensitive drums, development roller, and the like can beassumed as banding sources as long as they are rotation membersassociated with image formation.

Explanation of General Arrangement of Motor

First of all, in FIGS. 3A to 3C respectively show, as an example, asectional view of the motor 6, a front view of the motor 6, and anextracted view of a circuit board 303. Note that the motors 6 can bemade equivalent to various motors included in the imaging forming unitssuch as the motors 6 a to 6 d which drive the photosensitive drums 22described above and the motor 6 e which drives the driving roller 52.

Referring to FIGS. 3A and 3B, a rotor magnet 302 formed from a permanentmagnet is bonded to the inner side of a rotor frame 301. Coils 309 arewound around stators 308. The plurality of stators 308 are arrangedalong the inner circumferential direction of the rotor frame 301. Ashaft 305 transmits rotational force outside. More specifically, theshaft 305 is fabricated into a gear or a gear made of a resin such asPOM is fitted on the shaft 305 to transmit rotational force to a matinggear. Bearings 306 are fixed to a housing 307, which is fitted in amount plate 304.

An FG patch (speed patch) 310 is printed in an annular form on thesurface, of the circuit board 303 shown in FIG. 3C, which is located onthe rotor side so as to face an FG (Frequency Generator) magnet 311.Circuit components (not shown) for driving control are mounted on theother surface of the circuit board 303. The circuit components fordriving control include a control IC, a plurality of (for example,three) Hall elements, resistor, capacitor, diode, and MOSFET. Thecontrol IC (not shown) rotates the rotor frame 301 and each partconnected to it by switching the coils in which a current is to flow andthe direction of the current based on the position information (Hallelement outputs) of the rotor magnet 302.

FIG. 3D shows an extracted view of the rotor magnet 302. The innersurface of the rotor magnet 302 is magnetized in the manner indicated byreference numeral 312, and the open end face of the rotor magnet 302 ismagnetized by the FG magnet 311. In this embodiment, the rotor magnet302 has driving magnetizations of eight poles (four N poles and four Spoles). Ideally, the N- and P-pole magnetizations 312 are alternatelyarranged. On the other hand, the FG magnet 311 is magnetized into N andS poles larger in number than the driving magnetizations (in thisembodiment, 32 pairs of N and S poles). Note that the FG patch 310indicated by FIG. 3C has rectangles equal in umber to the magnetizationsof the FG magnet 311, which are connected in series in an annular form.Obviously, the numbers of driving magnetizations and FG magnets are notlimited to those described above, and they can be applied in otherforms.

The motor exemplified by FIGS. 3A to 3E uses, as a speed sensor for themotor, a sensor of the frequency generator system of generating afrequency signal proportional to a rotational speed, that is, the FGsystem. This system will be described below. When the FG magnet 311rotates integrally with the rotor frame 301, a sine wave signal having afrequency corresponding to a rotational speed is induced in the FG patch310 due to magnetic flux changes relative to the FG magnet 311. Thecontrol IC (not shown) generates a pulsed FG signal by comparing thegenerated inductive voltage with a predetermined threshold. The controlIC then performs speed/driving control on the motor 6 and various kindsof processes (to be described later) based on the generated FG signal.Note that a speed sensor for the motor is not limited to the frequencygenerator type, and it is possible to use an encoder type sensor such asan MR sensor or slit-plate type sensor.

Although described later, it is assumed that in this embodiment, therotation unevenness of the motor is linked to density unevenness(banding). That is, when predicting what kind of periodic densityunevenness is generated, this apparatus uses the rotation phase of therotation unevenness of the motor as a parameter. The CPU 401 (to bedescribed later) specifies the rotation phase of rotation unevennessbased on the FG signal output from the motor 6.

Mechanism of Generation of Rotation Unevenness of Motor

In general, the form of rotation unevenness of a one-rotation period ofthe motor is determined by the structure of the motor. Typically, forexample, the form of rotation unevenness of a one-rotation period of themotor is determined by two factors including the magnetized state of therotor magnet 302 (magnetization fluctuations corresponding to onerotation of the rotor) and the offset between the center positions ofthe rotor magnet 302 and stator 308. This is because the total motordriving force generated by all the stators 308 and all the rotor magnets302 changes during one period of the motor 6 due to the two factors.Fluctuations in magnetization will be described below with reference toFIG. 3E. FIG. 3E shows a view of the magnetizations 312 when viewed fromthe front. Reference symbols A1 to A8 and A1′ to A8′ denote theboundaries where the poles change. The boundaries A1 to A8 plotted atequal intervals along the circumference indicate the boundaries betweenthe N and S poles without any magnetization fluctuations. The boundariesA1′ to A8′ indicate the boundaries between the N and S poles withmagnetization fluctuations.

In addition, the decentering of the motor shaft (pinion gear) 305 can becounted as one factor for the rotation unevenness of the motor. Thisrotation unevenness is transmitted to the rotating mating part. Thisunevenness appears as density unevenness. The decentering of the motorshaft (pinion gear) 305 also depends on a one-rotation period of themotor 6. The rotation unevenness obtained by combining this rotationunevenness with the rotation unevenness due to the above magnetizationfluctuations is transmitted to the driving power destination, andappears as density unevenness. This is the typical mechanism of theoccurrence of rotation unevenness of a one-rotation period of the motor.

In addition, the motor 6 also produces rotation unevenness of a periodother than the above rotation unevenness of a one-rotation period. Inthe motor having eight driving magnetic poles magnetized on the rotormagnet 302, the respective Hall elements (not shown) detect magneticflux changes corresponding to four periods per rotation of the motorbecause of the four pairs of N and S poles. If the position of any ofthe Hall elements shifts from the ideal position, the phase relationshipbetween outputs from the respective Hall elements deteriorates with aone-period magnetic flux change. Consequently, the switching timingshifts in the motor driving control operation of switching excitation tothe coil wound around the stator based on outputs from the respectiveHall elements. This causes rotation unevenness of a ¼ period of aone-rotation period of the motor 6 four times during one rotation of themotor 6. Obviously, this causes rotation unevenness of a period of afraction of an integer (a frequency of an integer multiple)corresponding to the number of poles of driving magnetizations of therotor magnet 302.

<Hardware Arrangement Associated with Signal Processing>

A hardware arrangement associated with signal processing will bedescribed next with reference to FIG. 4. In this case, a density signalprocessing unit 405 and an FG signal processing unit 406 each are formedfrom, for example, an application specific integrated circuit (ASIC) orSOC (System On Chip). The CPU 401 performs various control operations incooperation with the respective blocks, namely a storage unit 402, animage forming unit 403, the FG signal processing unit 406, the densitysignal processing unit 405, and the density sensor 51. The CPU 401 alsoperforms various kinds of computation processing based on inputinformation.

The storage unit 402 includes an EEPROM and a RAM. The EEPROM stores thecorrespondence relationship between a count value (corresponding to aphase signal from the motor) identifying an FG signal as a phase signalfrom the motor 6 and correction information for correcting image densityin a rewritable form. The EEPROM also stores other kinds of settinginformation used for image formation control by the CPU 401. The RAM ofthe storage unit 402 is used to temporarily store information when theCPU 401 executes various kinds of processing. The image forming unit 403is a generic term of each member associated with the image formationdescribed with reference to FIG. 1. A detailed description of this unitwill be omitted. The density sensor 51 is the same as that describedwith reference to FIG. 2.

The density signal processing unit 405 receives a density detectionsignal from the density sensor 51, and supplies (outputs) the inputsignal to the CPU 401 without or with processing to allow the CPU 401 toeasily extract density unevenness associated with the motor 6 ofinterest. On the other hand, the FG signal processing unit 406 receivesthe FG signal output from the motor 6, described with reference to FIGS.3A to 3E, and performs processing associated with the FG signal. Forexample, the FG signal processing unit 406 processes the FG signal toallow the CPU 401 to specify the phase of the motor, and outputs theprocessed signal to the CPU 401, or notifies the CPU 401 of thedetermination result on processing associated with the FG signal.

According to this embodiment, the CPU 401 creates a table associatingthe rotational phase of the motor and correction information for densitycorrection (banding correction) based on the density signal output fromthe density signal processing unit 405 and the phase signal output fromthe FG signal processing unit 406. The CPU 401 also causes a scannerunit 24 to perform exposure reflecting image correction in accordancewith the phase of rotation unevenness of the motor 6 in synchronism witha change in the phase of the motor 6 which is specified based on the FGsignal supplied from the FG signal processing unit 406. The details ofthis operation will be described with reference to the flowchartdescribed later.

<Arrangement of Density Signal Processing Unit 405>

The density signal processing unit 405 described with reference to 4 ain FIG. 4 will be described in detail next with reference to 4 b in FIG.4. A low-pass filter (LPF) 407 selectively transmits a signal of aspecific frequency component. The cutoff frequency of the filter is setto mainly transmit signals equal to or less than a frequency component(to be referred to as a W1 component hereinafter) in one rotation of themotor and attenuate a signal of a frequency of an integer multiple ofthe W1 component. In FIG. 5, 5 a shows an example of the operation ofthe LPF. Causing a density sensor output to pass through the LPF caneasily extract the density unevenness of the W1 component.

A bandpass filter (BPF) 408 can extract a predetermined frequencycomponent from an output from the density sensor 51. For example, thisembodiment is configured to extract rotation unevenness of a frequencyfour times the frequency of one rotation of the motor (¼ period: to bereferred to as a W4 component hereinafter). For the filtercharacteristics, two cutoff frequencies are provided on the two sides ofthe frequency of a W4 component. In FIG. 5, 5 b shows an example of theoperation of the BPF. Causing a density sensor output to pass throughthe BPF can easily extract density unevenness of a W4 component.

The density signal processing unit 405 also supplies, to the CPU 401,raw sensor output data which is a detection result from the densitysensor 51 from which no rotation unevenness component of the motor isremoved. For example, the CPU 401 uses this raw sensor output data whencalculating the average detection value of the density sensor 51.

Although described in later, the CPU 401 in this embodiment calculates acorrection value for correcting density unevenness based on both a W1component and a W4 component due to the rotation unevenness of themotor. The storage unit 402 stores the calculated correction value inassociation with the count value of an FG signal as a phase signal toallow the use of the correction value in accordance with the rotationphase of the motor 6 at the time of image formation (exposure). In thiscase, it is possible to associate the phase of the rotation unevennessof the motor 6 with a given state in the periodic rotational speedvariations of the motor 6. A change in the phase of the rotationunevenness of the motor indicates a change in the speed of the motor 6from a previous given speed state.

<Arrangement of FG Signal Processing Unit 406>

The FG signal processing unit 406 described with reference 4 a in FIG. 4will be described in detail next with reference to 4 c in FIG. 4. An F/Vconverter 409 performs frequency analysis of an acquired FG signal. Morespecifically, the FG signal processing unit 406 measures the pulseperiod of the FG signal, and outputs a voltage corresponding to theperiod. The cutoff frequency of a low-pass filter 410 is set to transmitfrequencies equal to or less than a W1 component and attenuatefrequencies higher than a W1 component. Note that the FG signalprocessing unit 406 may be provided with an FFT analysis unit, in placeof the F/V converter 409 and the low-pass filter 410, to performfrequency analysis of an FG signal. An SW 411 is a switch for switchingwhether to input the signal output from the low-pass filter 410 to adetermination unit 412. An SW control unit 413 turns on the SW 411 inaccordance with an initialization signal, and turns off the SW 411 inaccordance with an FG counter signal input next after the completion ofresetting operation.

The determination unit 412 acquires signals corresponding to one periodof the motor, which are input from the low-pass filter 410, andcalculates the average value of the signals. Upon calculating theaverage value, the determination unit 412 compares the average valuewith the value input from the low-pass filter 410, and outputs a counterreset signal when a predetermined condition holds. The counter resetsignal is input to the SW control unit 413 and an FG counter 414. Inaddition, the counter reset signal is sent to the CPU 401 to notify itof the completion of resetting operation.

The FG counter 414 counts up the number of FG pulses corresponding toone period of the motor to perform toggling. In this embodiment, whenthe motor makes one rotation, an FG signal having 32 pulses is output.The FG counter 414 counts 0 to 31. In addition, upon receiving a counterreset signal, the FG counter 414 resets to “0”.

<Main Hardware Arrangement and Function Arrangement>

The main hardware arrangement and function arrangement of thisembodiment will be described next with reference to (a) in FIG. 6. InFIG. 6, 6 a shows the relationship between some members of the imageforming apparatus, some of the block diagrams shown in FIG. 4, and thefunctional block diagram controlled by the CPU 401. Note that the samereference numerals denote the same components in FIGS. 1 and 4, and adetailed description of them will be omitted.

Referring to 6 a in FIG. 6, a test patch generation unit 35 functions asa patch forming unit and controls a forming function for a patch image(to be referred to as a test patch hereinafter) 39 formed by a tonerimage for the detection of a density on the intermediate transfer member27. The test patch generation unit 35 forms an electrostatic latentimage on the photosensitive drum 22 by the scanner unit 24 based on thedata of a test patch. The test patch generation unit 35 then forms atoner image (test patch) based on the electrostatic latent image formedby a developing unit (not shown) on the intermediate transfer member 27.The density sensor 51 irradiates the test patch 39 formed on theintermediate transfer member 27 with light, detects the reflected lightcharacteristic of the light, and inputs the detection result to thedensity signal processing unit 405.

A correction information generation unit 36 generates density correctioninformation based on the detection result on the test patch 39 which isdetected by the density sensor 51. This operation will be described indetail later with reference to FIGS. 11A to 11C. An image processingunit 37 executes image processing such as halftone processing forvarious types of images. The arrangement of the image processing unit 37will be described later. An exposure control unit 38 causes the scannerunit 24 to perform exposure in synchronism with an FG count value toform a test patch on the intermediate transfer member 27 through anelectrophotographic process.

The form shown in FIGS. 4 and 6 a in FIG. 6 is an example, and thepresent invention is not limited to this arrangement example. Forexample, it is possible to make an application specific integratedcircuit bear some or all of the functions born by the CPU 401 in FIGS. 4and 6 a in FIG. 6. In contrast to this, it is possible to make the CPU401 bear some or all of the functions born by the application specificintegrated circuit in FIGS. 4 and 6 a in FIG. 6.

<Arrangement of Image Processing Unit 37>

An example of the arrangement of the image processing unit 37 will bedescribed next with reference to 6 b in FIG. 6. When printing operationstarts in response to a print instruction from a host computer or thelike, a color matching processing unit 701 performs color conversionprocessing by using a color matching table prepared in advance. Morespecifically, the color matching processing unit 701 converts an RGBsignal representing the color of the image sent from the host computerinto a device RGB signal (to be referred to as DevRGB hereinafter) inaccordance with the color reproduction region of the image formingapparatus. A color separation processing unit 702 converts the DevRGBsignal into a CMYK signal representing the color of a toner (coloringmaterial) in the imaging forming apparatus.

A density correction processing unit 703 reads a density correctiontable for correcting tone/density characteristics stored in the storageunit 402 in accordance with an instruction from the CPU 401, andconverts the above CMYK signal into a C′M′Y′K′ signal having undergonetone/density characteristic correction by using this density correctiontable. In this embodiment, the C′M′Y′K′ signal has a data length of 8bits.

Subsequently, a halftone processing unit 704 performs halftoneprocessing for the C′M′Y′K′ signal. The halftone processing unit 704performs multilevel dither processing, and converts the input 8-bitsignal into a 4-bit C″M″Y″K″ signal. Thereafter, an image correctionunit 705 which performs banding correction (to be described later)performs banding correction processing to obtain a 4-bit C″′M″′Y″′K″′signal. According to this embodiment, the image correction unit 705converts a 4-bit (m-bit) image signal after halftone processing into an8-bit (n-bit) expression, and then executes banding image correction.Thereafter, the image correction unit 705 quantizes the 8-bit correctionsignal into a 4-bit correction signal. In this case, this embodimentdisperses quantization errors so as to cancel them in a predeterminedregion including a plurality of continuous pixels for each main scanningline. These methods will be described in detail later. A PWM processingunit 706 converts the above C″′M″′Y″′K′″ signal into exposure times Tc,Tm, Ty, and Tk of the scanner units 24C, 24M, 24Y, and 24K by using aPWM (Pulse Width Modulation) table.

<Output Correction Table Creation Processing>

A procedure for output correction table creation processing will bedescribed next with reference to FIG. 7. The processing described abovewill specify the correspondence relationship between phase signals fromthe motor and density unevenness, compute density correction informationfor the density unevenness, and create a correspondence table betweenthe phase signals from the motor and density correction information. Thecreated table is used to reduce banding at the time of the subsequentexecution of printing. This operation will be described in detail below.

First of all, in step S801, a motor control unit 40 starts processing inan output correction adjustment mode. In step S802, the motor controlunit 40 checks whether the motor falls within a predetermined range ofnumbers of revolutions. Upon checking this, the motor control unit 40changes the setting of a control gain 42 of a speed control unit 43 tothe minimum value. Note that in gain setting, it is possible to set thegain to at least a set value lower than that in normal image formingoperation instead of the minimum value. Setting the gain in this mannerwill increase rotation unevenness corresponding to a one-rotation periodof the motor, thereby facilitating the detection of the unevenness. Inthis case, the normal image forming operation indicates, for example,image forming operation based on the image information which is inputfrom a computer outside the image forming apparatus and is created inaccordance with user's computer operation.

Subsequently, in step S803, the CPU 401 turns on the SW 411 via the SWcontrol unit 413 to start counting a motor FG signal in order to detectthe rotational phase of the motor. In step S804, the determination unit412 extracts outputs from the F/V converter 409, that is, rotationunevenness corresponding to a one-rotation period of the motor which hasbeen processed by the LPF 410, and averages them.

In step S805, the determination unit 412 determines whether the motorrotation unevenness phase of a W1 component has become a predeterminedphase. In this case, the determination unit 412 checks whether therotation unevenness phase of the motor 6 has become 0. Upon determiningYES in step S805, the determination unit 412 issues a counter resetsignal to reset the FG counter 414 in step S806. In step S806, the CPU401 starts observing the count of an FG signal as a motor phase signal.The count of the FG signal specifies the phase of the motor 6. The CPU401 keeps observing the count value of the FG signal to the end of aprint job.

In step S807, the motor control unit 40 returns the setting of thecontrol gain 42 from the minimum value to the initial set value. Thisoperation can set the same condition as that in normal image formingoperation in terms of the control gain 42 in test patch formingoperation. In step S808, the test patch generation unit 35 generatestest patch data for the patch 39.

In step S809, the test patch generation unit 35 determines whether thecount value of the FG signal from the motor has become a predeterminedvalue (for example, “0”). If YES in step S809, the test patch generationunit 35 causes the scanner unit 24 to start performing exposure using instep S810. Note that this apparatus performs no image correction at thetime of the formation of a test patch. More specifically, the test patchgeneration unit 35 forms a pre-patch and a normal patch at this time. Inthis case, a pre-patch is formed at a position preceding a normal patchby a predetermined distance to generate the timing to start measuringthe density of the normal patch by the density sensor 51. The normalpatch has a length corresponding to one rotation of the motor 6 in thesub scanning direction.

In step S811, the density sensor 51 detects reflected light obtainedfrom the test patch formed on the intermediate transfer member 27. Inthis case, the detection result obtained by the density sensor 51 isinput to the CPU 401 via the density signal processing unit 405. Threekinds of signals are input to the CPU 401, as described with referenceto 4 b in FIG. 4.

The correction information generation unit 36 functions as a correctionamount determination unit. In step S812, the correction informationgeneration unit 36 calculates density correction information forreducing density unevenness due to the rotation unevenness of the motorbased on the detection result obtained in step S811. In addition, thecorrection information generation unit 36 stores the calculated densitycorrection information in the EEPROM. In the processing in step S811, asdescribed with reference 4 b in FIG. 4, the LPF 407 and the BPF 408respectively detect W1 and W4. Note that the start timing of thedetection of reflected light from the W4 component is the same as thatfrom the W1 component. In step S812, the correction informationgeneration unit 36 computes correction information for correcting theunevenness of each of the W1 and W4 components based on the densityunevenness of the W1 and W4 components. Upon completing the processingin each step described above, the apparatus terminates the processingfor exposure output correction table creation in step S813.

<Processing of Associating Motor Phase with Density Variation of TonerImage>

The processing in steps S802 to S806 in FIG. 7 will be described indetail next with reference to FIG. 8. FIG. 8 is a timing chart showingan embodiment of reset processing for a motor FG counter value. Thetiming chart shown in FIG. 8 allows to determine which speed variationstate of the motor 6 is to be associated which phase (phase zero (FG 0)in this case). In the case shown in FIG. 8, a state in which the speedof the motor crosses the average value in the process of changing from aspeed higher than the average to a speed lower than the average isassigned to phase zero (FG 0). Note the case shown in FIG. 8 is anexample, and it is possible to assign an arbitrary or predeterminedspeed variation state of the motor 6 to any phase (for example, phasezero (FG 0)). That is, an arbitrary or predetermined speed state of themotor 6 may be assigned to any phase (arbitrary or predetermined phase)of the motor 6, on the premise of reproducibility, so as to allow thephase assigned with the state to be specified in subsequent processing.This makes it possible to perform various types of processing at othertimings by using any phase of the motor 6 as a parameter. This operationwill be described in detail below.

First of all, when the CPU 401 outputs an initialization signal to theFG signal processing unit 406 at t0, and the signal is transmitted tothe SW control unit 413. The SW control unit 413 turns on the SW 411 insynchronism with the FG signal input first after t0 (S803).

In the interval between t1 and t2 (corresponding to one rotation of theFG signal motor), the determination unit 412 calculates an average valueVave input values from the low-pass filter 410. The determination unit412 compares the average value Vave with the value input from thelow-pass filter 410 after t2, and outputs a counter reset signal attiming t3 (YES in step S805) at which a predetermined condition holds,for example, the input value crosses the average value Vave in theprocess of changing from a value larger than the average value to avalue smaller than the average value. Upon receiving a counter resetsignal at timing t3, the FG counter 414 resets the count to “0” (S806).Upon receiving the counter reset signal, the CPU 401 recognizes thecompletion of the initialization of a phase signal (FG count value).

The exposure timing for a patch image (test patch), that is, theprocessing in step S808 in FIG. 7, will be described in detail next withreference to 9 a in FIG. 9. Assume that in the timing chart of 9 a inFIG. 9, the CPU 401 keeps counting the FG signal from the processing inFIG. 8. That is, this operation is based on the premise that the CPU 401continuously specifies the rotation unevenness phase of the motor 6 inaccordance with changes in FG counter value. The details of theprocessing shown in 9 a in FIG. 9 will be described below.

A test patch will be defined in detail first. As described above, thetest patch includes a pre-patch for the generation of a read timing anda normal patch for density unevenness measurement. The test patchgeneration unit 35 starts forming (exposing) a pre-patch at timing t4(an FG count of 10 before exposure of a normal patch in this embodiment)before the counter reaches a predetermined FG count value correspondingto the time to start expose a normal patch. A pre-patch is used tosynchronize with the detection start timing of a test patch by thedensity sensor 51. The pre-patch may be short in the sub scanningdirection. For example, this patch need not have a length correspondingto a one-rotation period of the motor, and is only required to have alength long enough to be detected by the density sensor 51. In the caseshown in 9 a in FIG. 9, the exposure time for a pre-patch is set to theFG counter of 2, and exposure for the pre-patch is stopped at timing t5.

At timing t6, the test patch generation unit 35 starts performingexposure for a normal patch when the predetermined FG count becomes 0(S809). Thereafter, the test patch generation unit 35 continues exposureuntil the FG count becomes at least a value corresponding to one or morerotations of the motor (S810). The test patch generation unit 35 finallyforms a test patch as a toner image on the intermediate transfer member27 through the electrophotographic process described with reference toFIG. 1.

In FIG. 9, 9 b shows a timing chart for reading a test patch, withreference to which the details of the processing in step S811 in FIG. 7will be described. According to the description made with reference to 9a in FIG. 9, the test patch generation unit 35 starts performingexposure for a test patch after the FG count of 10 from the start ofexposure for a pre-patch. For this reason, the density sensor 51 readsthe test patch after the lapse of a time corresponding to the count of 9since reading the pre-patch. At t8, the density sensor 51 detects thepre-patch. The CPU 401 then starts reading the test patch at t10 when atime corresponding to the count of 9 has elapsed since timing t9 of thedetection of the next FG pulse. Referring to 9 b in FIG. 9, referencenumeral 1001 denotes an FG signal as a phase signal from the motor 6which is obtained by exposing the normal test patch to read opticalcharacteristics under the control of the CPU 401 and is recognized bythe CPU 401. FIG. 10 schematically shows how this signal is obtained.

In FIG. 10, 10 a to 10 c schematically show the relationship between theexposure timing of the scanner unit 24 and the phase signal from themotor 6 which is recognized by the CPU 401 at the same timing. In FIG.10, 10 a and 10 b show how the CPU 401 recognizes the phase signal fromthe motor 6 when forming an electrostatic latent image on a test patch.Referring to FIG. 10, FGs1 and FGs2 respectively correspond to phases θ1and θ2. In FIG. 10, 10 c is a view showing which phase signals from themotor 6 at the time of image exposure correspond to the respectivepositions along the moving direction of the formed test patch. The CPU401 also manages the correspondence relationship shown in 10 c.

Although not shown in 9 b in FIG. 9, in practice, the BPF also outputs asignal obtained by detecting the optical characteristics of a W4component in synchronism with timing t10, and inputs it to the CPU 401.The density signal processing unit 405 then inputs the opticalcharacteristics of the test patch obtained by the density sensor 51 tothe CPU 401 through the LPF 407 and the BPF 408. The CPU 401 stores theoptical characteristic value (corresponding to a density value) outputfrom the density signal processing unit 405 and the phase signal (FGcount value) from the motor 6 at the time of the formation of a patch tobe detected in the EEPROM in association with each other. Upon reachingtiming t11 and obtaining a detection result by the density sensor 51which corresponds to an FG count corresponding to at least one rotationof the motor, the CPU 401 terminates the test patch reading operation.

<Density Unevenness Component of Test Patch>

As is understood from FIG. 10, the detection result on the test patchincludes the influence of the rotation unevenness of the motor 6 at thetime of exposure and the influence of the rotation unevenness of themotor 6 at the time of transfer. In this case, the source of rotationunevenness at the time of exposure is the same as that at the time oftransfer. As described above, rotation unevenness reflecting theintegrated influence is detected from a test patch. Note that sincedensity unevenness is due to the physical shape of the motor, therotation unevenness phase of a one-rotation period of the motor isreproducible in correspondence with the physical shape of the motor.

<Example of Output Correction Table>

FIGS. 11A to 11C show examples of correction tables created inaccordance with the processing in step S812 in the flowchart of FIG. 7.The information shown in FIGS. 11A to 11C is stored in the EEPROM. Atthe time of image formation, the CPU 401 refers to this information toperform banding correction in accordance with the rotation unevennessphase of the motor.

Tables A in FIGS. 11A and 11B each show the correspondence between motorphases and the density values of a toner image. Referring to FIGS. 11Aand 11B, tables A are respectively created for W1 and W4. In this case,for W1, it is possible to calculate the density values indicated by FIG.11A by converting the voltage values V1 detected via the LPF 407 intodensity values. For W4, it is possible to calculate the density valuesindicated by FIG. 11B by converting the detection results obtained viathe BPF 408 into density values and adding average density values tothem. Note that it is possible to obtain average density values from thedetection results for W1 or by making the correction informationgeneration unit 36 average raw sensor output data indicated by 4 b inFIG. 4.

The correction information generation unit 36 then calculate differencesΔd1 and Δd2 between the respective density values and the respectiveaverage values for each of W1 and W4, and creates tables B byassociating the calculated differences Δd1 and Δd2 and the respectivephase signals. In this case, the average value is 10.000. The correctioninformation generation unit 36 then adds the respective phase signalsstored in table B and the corresponding differences Δd1 and Δd2 tosummate the difference values for W1 and W4. Table C indicated by FIG.11C is the resultant table.

The correction information generation unit 36 calculates a positioncorrection value for each main scanning line of an image based on thetotal difference value corresponding to each phase signal. Morespecifically, first of all, letting Dc_n be a density variation ratiocorresponding to FGn at a given phase of the motor 6, and Dave is anaverage density value, Dc_n is given as Dc_n=total differencevalue/Dave×100 (table D). The correction information generation unit 36then converts the correction value Dc_n into a position correctionamount Tc_n according to Tc_n=K×Dc_n (table E), where K is apredetermined coefficient which determines the correspondence between adensity variation ratio [%] and a position correction value [line] foreach image resolution in the sub scanning direction. In the case shownin FIGS. 11A to 11C, K=1.5. In addition, the unit of position correctionamount is dot, which represents how much a pixel signal is shiftedrelative to an adjacent line in the sub scanning direction. If thedensity variation ratios Dcn and the position correction values Tc_n donot have a proportional relationship, it is possible to hold therelationship between the density variation ratios Dcn and the positioncorrection values Tc_n in the form of a table and to convert Dc_n intoTc_n by using the table.

The correction information generation unit 36 then interpolates theposition correction value Tc_n between FG signals to create a positioncorrection value T_m for each main scanning line. More specifically,letting ΔT [sec] be the scanning interval between the respective mainscanning lines of image data, Mt [sec] be the time taken for onerotation of the motor, and n be an FG count corresponding to onerotation of the motor, the interval between FG signals, that is, theinterval between the output timings of FG signals (phase signals) isgiven by ΔFt=Mt/n. Therefore, the correction information generation unit36 interpolates data between the scanning intervals ΔFt by a method likea linear or spline interpolation method to generate data at theintervals ΔT (FIG. 12), thereby creating table F. For the sake ofsimplicity, FIG. 12 shows a case in which ΔFt=ΔT×3. As shown in FIG. 12,as the FG signal advances by one period, FG count=0 is set again torepeat the processing by the number of lines of one page of an image.With the above operation, it is possible to obtain a position correctionvalue for each line in the sub scanning direction.

The CPU 401 stores the calculated information of table F in the EEPROMso as to allow the reuse of the information. As described above, thisembodiment can cope with a case in which rotation unevennesses of aplurality of periods (frequencies) occur from one rotation member, thatis, the motor 6, and affect banding, thereby finely handling thesituation.

The relationship between FG counter value and exposure timing at thetime of image formation will be described next with reference to FIG.13. For the sake of simplicity, assume that the same motor drives thephotosensitive drums 22Y, 22M, 22C, and 22K of the respective colors,namely Y, M, C, and K. The apparatus starts image data correctionprocessing (to be described later) for a Y image of the first color attime tY11, and starts exposure for the Y image at the timing (time tY12)when the FG counter value becomes 0. At time tM11, the apparatus startsimage data correction processing (to be described later) for an M imageof the second color, and starts exposure for the M image at time tY21when tYM has elapsed after the exposure for the Y image. In this case,tYM represents the time difference that is adjusted in advance toeliminate the difference in placement position between thephotosensitive drums 22Y and 22M so as to match the position of the Yimage with that of the M image in the conveying direction. An FG countervalue FGm at time tM12 may be calculated according to tYM/ΔFt in advancebefore image formation, and a correction table for M may be created inadvance with reference to FGm. The same applies to C and M. Obviously,when different motors drive the photosensitive drums 22Y, 22M, 22C, and22K of Y, M, C, and K, it is possible to perform processing similar tothat described above by acquiring the FG count value of the motor ofeach color by a method similar to that described above. Note that thecorrection processing of image data will be described in detail later.

<Image Data Correction>

An image correction process and a correction amount modification processin the image correction unit 705 will be described next with referenceto FIGS. 14 and 15. The image correction process will be described firstwith reference to FIG. 14. The image signal processed by the halftoneprocessing unit 704 is temporarily loaded in the line buffer (inputimage buffer) in the storage unit 402. Assume that in this embodiment,the input image buffer has a size corresponding to one page. At the sametime, assume that a corrected image buffer and an output image buffereach having the same size as that of the input image buffer are ensuredin the storage unit 402. The input image buffer stores 4-bit pixelvalues like those indicated by (a) in FIG. 17 which have undergonehalftone processing.

First of all, in step S1401, the image correction unit 705 converts4-bit pixel values Q4 _(—) n=0 to 15 stored in the input image bufferinto 8-bit values Q8 _(—) n=0 to 255, as shown in (b) in FIG. 17. Instep S1402, the image correction unit 705 then performs initializationto clear the corrected image buffer to 0.

In step S1403, the image correction unit 705 sets line number m=0 andaccumulative position correction amount TL_0=0 for a first main scanningline L_0. In addition, since the apparatus starts exposure for imagedata at the timing when an FG count value FGs becomes 0, the imagecorrection unit 705 sets the position correction value T_m for a lineL_m.

The image correction unit 705 then performs corrections for the mainscanning line L_m. A method of correcting the main scanning line L_mwill be described below. First of all, in step S1404, the imagecorrection unit 705 reads the position correction value T_m for the mthline from the position correction table (FIGS. 11A to 11C), andcalculates an accumulative position correction amount TL_m for the mainscanning line L_m from an accumulative position correction amount TL(m−1) for the (m−1)th line and the position correction value T_m by thefollowing processing: TL_m=TL_(m−1)+T_m. Subsequently, the imagecorrection unit 705 corrects the input image signal. The imagecorrection unit 705 performs this correction to shift the image signalcorresponding to the line L_m by TL_m lines.

First of all, in step S1405, the image correction unit 705 obtains acorrection amount by the following equations:

y1=ceil(TL _(—) m)

y2=y1−1

r1=1.0−(y1−TL _(—) m)

r2=1.0−r1

where ceil represents rounding to an integer in a positive infinitedirection.

In step S1406, the image correction unit 705 initializes a pixel numberk in the main scanning direction to 0. In step S1407, the imagecorrection unit 705 corrects the image signal according to the followingequations:

I′(m+y1,k)=I′(m+y1,k)+r1×I(m,k)

I′(m+y2,k)=I′(m+y1,k)+r2×I(m,k)

where I(m, k) represents the value of a pixel, in the input imagebuffer, which is located at the mth sub scanning line and the kth mainscanning line, and I′(m, k) represents the value of a pixel, in thecorrected image buffer, which is located at the mth sub scanning lineand the kth main scanning line.

The contents of the processing based on the above equations will bedescribed with reference to 18 a and 18 b in FIG. 18. As shown in FIG.18, when position correction amount TL_m=1.3 [line] for the main lineL_m, the image correction unit 705 shifts the line L_m by 1.3 lines inthe sub scanning direction. In this case, line-based shift amount=1 lineand shift amount of less than 1 line=0.3 lines. The image correctionunit 705 performs correction of a shift amount of less than 1 line bydistributing pixel values to two lines. For example, in the case ofTL_m=1.3 [line], y1=2, y2=1, r1=0.3, and r2=0.7. With regard to the twolines, m+y1 indicates the line on the downstream side in the subscanning direction, and m+y2 indicates the line on the upstream side inthe sub scanning direction. In addition, r1 indicates a weight assignedto the (m+y1)th line, and r2 indicates a weight assigned to the (m+y2)thline.

Consider an input pixel value I(y, k) on the line L_m in 18 a in FIG.18. In this case, the image correction unit 705 adds the value obtainedby multiplying the value of an image signal I(m, k) on the mth line inthe input image buffer by r1=0.3 to a pixel value I′ (m+2, k) on the(m+y1)th=(m+2)th line in the corrected image buffer. In addition, theimage correction unit 705 adds the value obtained by multiplying thevalue of the image signal I(m, k) on the mth line in the input imagebuffer by r2=0.7 to a pixel value I′ (m+1, k) on the (m+y2)th=(m+1)thline on the output image buffer. With this operation, pixel values likethose shown in 18 b in FIG. 18 are added to lines L_(m+1) and L_(m+2) inthe corrected image buffer.

In step S1408, the image correction unit 705 determines whether theprocessing is completed for all the pixels within the line. If NO instep S1408, the image correction unit 705 increments k by one in stepS1410. The flow then shifts to step S1407 again. If the image correctionunit 705 determines in step S1408 that the processing is completed forall the pixels, the process advances to step S1409. With the aboveprocessing, the image correction unit 705 performs position correctionwith respect to the line L_m.

In step S1409, the CPU 401 determines whether the processing iscompleted for a predetermined main scanning line (the last main scanningline within the page). If NO in step S1409, the image correction unit705 increments m by one in step S1411 to execute the processing in stepS4104 for the next main scanning line. Upon completing for apredetermined number of main scanning lines and determining YES in stepS1409, the CPU 401 terminates the image correction process. The processthen shifts to the next correction amount modification process. Notethat in the image correction process, an output image signal correspondsto the first correction image signal.

The correction amount modification process will be described next withreference to FIG. 15. In the correction amount modification process, theimage correction unit 705 converts 8-bit data in the corrected imagebuffer into 4-bit data, and stores the data in the output image buffer.The image correction unit 705 sets the pixel values on the line L_m inthe corrected image buffer to P_0, P_1, . . . from the left end in thescanning direction, and sets the kth pixel value to P_k. First of all,in step S1501, the image correction unit 705 sets m=0. In S1502, theimage correction unit 705 initializes a difference E to 0, and sets mainscanning number of pixel of interest k=0. Thereafter, the imagecorrection unit 705 performs modification for the main scanning lineL_m. First of all, the image correction unit 705 adds the difference Eto P_k (P′_k=P_k+E) to obtain P′_k in step S1503.

In step S1504, the image correction unit 705 performs quantization to4-bit values. In this case, as for each 4-bit value, the imagecorrection unit 705 expresses a 4-bit value Q8 _(—) n nearest to P′_k asa quantized signal Pq_k by using a value Q8 _(—) n in an 8-bitexpression described above. The image correction unit 705 can performquantization according to the following equation:

Pq _(—) k=floor((P′ _(—) k+8)/17)×17

where floor represents rounding to an integer in a negative infinitedirection.

In step S1505, the image correction unit 705 functions as a differencecalculation unit and calculates the difference (quantization error)between values before and after the quantization, as E, by

E=P′ _(—) k−Pq _(—) k

In step S1506, the image correction unit 705 converts data in the 8-bitexpression into data in the 4-bit expression (conversion from Q8 _(—) nto Q4 _(—) n), and stores, in the output image buffer, a value Q_k afterthe conversion as an output image signal representing the pixel ofinterest, thereby completing the processing for the pixel of interest.

In step S1507, the image correction unit 705 determines whether theprocessing is completed for all the pixels within the line. If NO instep S1507, the image correction unit 705 increments k by one in stepS1509. The process then shifts to step S1503 again. Upon determining instep S1507 that the processing is completed for all the pixels, theimage correction unit 705 determines next in step S1508 whether theprocessing is completed for a predetermined main scanning line (the lastmain scanning line within the page). If NO in step S1508 the imagecorrection unit 705 increments m by one in step S1510. The process thenshifts to the processing in step S1502. If the processing is completedfor a predetermined number of main scanning lines and the CPU 401determines YES in step S1508, the correction amount modificationprocessing is completed for one page. Note that the image signal outputin the correction amount modification process corresponds to the secondcorrected image signal.

The manner of performing a series of processing operations in stepsS1503 to S1506 will be described with reference to 18 c in FIG. 18.Referring to 18 c in FIG. 18, reference numeral 1801 denotes values onthe line L_m in the corrected image buffer. The first pixel of interestis P_0=48, and E is 0 because it is initialized. With the processing instep S1503, therefore, P′_k=48. In step S1504, the image correction unit705 performs quantization to obtain Pq_k=(floor(48+8)/17)×17=51. In stepS1505, difference E=48−51=−3. In step S1506, the image correction unit705 performs conversion of 51→3 (conversion from data in the 8-bitexpression to data in the 4-bit expression; conversion from 51 to 3 inFIG. 17). As a result, output value Q_0=3.

The process then shifts the processing for P_1. Since P_1=179,P′_1=P_1+E=179−3=176 in step S1503. In step S1504,Pq_k=(floor(176+8)/17)×17=170. In step S1505, difference E=176−170=6. Instep S1506, the image correction unit 705 performs conversion of 170→10to obtain output value Q_1=10. The image correction unit 705sequentially performs processing while shifting the pixel of interest inthe scanning direction in the above manner. This diffuses thequantization error between the quantized signal Pq_k of each pixel onthe main scanning line and the value P_k before quantization within themain scanning line, thereby greatly reducing the sum total ofquantization errors within the main scanning line.

<Synchronization Between Image Data and FG Pulse>

Synchronization between image data and an FG pulse will be describednext with reference to FIG. 16. The CPU 401 starts the processing in theflowchart of FIG. 16 in association with the correction amountmodification process in FIG. 15.

First of all, when starting printing operation in step S1601, the CPU401 determines in step S1602 whether the correction amount modificationprocess is complete. If NO in step S1602, the CPU 401 waits until thecompletion of the process. Upon completion of the correction amountmodification process and determining YES in step S1602, the CPU 401determines in step S1603 whether the current processing is for the firstpage in the print job. Upon determining that the processing is for thefirst page, the CPU 401 executes reset processing for the motor FGcounter value (initialization processing for a phase signal) describedwith reference to FIG. 8 in step S1604. This reset processing makes itpossible to reproduce the association of the speed variation state ofthe motor 6 with a phase of the motor 6 at a predetermined timingdetermined by the timing chart of FIG. 8. Thereafter, the CPU 401specifies (monitors) the phase change of the motor by using the FG countvalue as a parameter. This makes it possible to cause the scanner unit24 to perform exposure for the cancellation of the rotation unevennessof the motor 6 in synchronism with the specified phase change of therotation unevenness phase of the motor 6 in the next step.

In step S1605, the CPU 401 specifies the phase change of the rotationunevenness of the motor 6. When the phase of the rotation unevenness ofthe motor 6 becomes an FG count value of 0, the CPU 401 causes thescanner unit 24 to start exposure in synchronism with this operation,thereby performing image formation. In step S1605, the scanner unit 24performs exposure upon image correction in accordance with the phase ofthe rotation unevenness of the motor. In this case, establishingsynchronization between an FG count value of 0 and the start timing ofexposure in the above manner will match a correction phase with abanding phase in the image correction process and the correction amountmodification process. It is therefore possible to effectively reducebanding. Subsequently, the CPU 401 determines in step S1606 whether theprocessing is completed for all the pages. If YES in step S1606, the CPU401 terminates the processing.

As described above, according to the above embodiment, it is possible toreduce density unevenness due to the rotation unevenness of the motor.In addition, when considering the rotation unevenness of the motor 6,similar banding does not always occur at the same position on a printingmedium P. However, the above embodiment can cope with such a case andproperly perform correction of density unevenness (banding). For thesake of descriptive convenience, the embodiment is configured to have apage memory corresponding to one page. However, to save the memory, theembodiment may be configured to have only a line buffer corresponding tothe number of lines required. In addition, to prevent quantized signalshaving the same value from continuing in the sub scanning direction, itis possible to interchange pixel numbers from which a correction amountmodification process starts for each line. As described above, a beltdriving roller, photosensitive drums, development roller, and the likecan be assumed as banding sources as long as they are rotation membersassociated with image formation. The correction described above is notlimited to banding correction, and can be applied to correction otherthan banding correction.

The relationship between a correcting direction and a direction todiffuse quantization errors and the effects will be described.

Diffusing quantization errors in the same direction as the correctingdirection (the sub scanning direction in this embodiment) will generatemany pixels containing the same quantization error at each main scanningposition within the same main scanning line. As a result, averagepositions corrected in the sub scanning direction on the overallscanning lines include many errors, resulting in noticeable streaks dueto the errors. This degrades the image quality. Furthermore, if thebanding period is short, since a correction amount changes at a highfrequency for each scanning line, the diffusion of errors cannot followup changes in correction amount, resulting in a great reduction inbanding reducing effect.

In contrast to this, as disclosed in this embodiment, diffusingquantization errors in the main scanning direction on each scanning linewill make average corrected positions in the sub scanning direction onthe overall scanning lines almost match the accuracy of 8 bits. Inaddition, even when the banding period is short, since there is noexchange of quantization errors between the respective scanning lines,it is possible to perform accurate correction. That is, it is possibleto effectively perform correction by diffusing quantization errors in adirection (the main scanning direction in this embodiment) perpendicularto the correcting direction (the sub scanning direction in theembodiment), as in the present invention.

Second Embodiment

The first embodiment described above performs modification in thecorrection amount modification process by adding the difference of apixel of interest to an adjacent pixel. The second embodiment willexemplify another correction amount modification method. Morespecifically, this embodiment modifies a correction amount so as tominimize a quantization error for each block including a plurality ofcontinuous pixels on the same main scanning line. Since the procedure upto the density correction in FIG. 14 is the same as that in the firstembodiment, a description of the procedure will be omitted. Arrangementsand techniques different from those in the above embodiment will bedescribed below.

A correction amount modification process in this embodiment will bedescribed first with reference to FIGS. 19A and 19B. When starting thecorrecting amount modification process, an image correction unit 705initializes a line number m to 0 in step S2001. In step S2002, the imagecorrection unit 705 initializes main scanning number k to 0. In stepS2003, the image correction unit 705 initializes an intra-block pixelnumber j to 0, and also initializes a sum total E_total of differenceswithin the block to 0.

Block-based processing then starts. In step S2004, the image correctionunit 705 quantizes a corrected image signal P_k to a 4-bit value toobtain Pq_k. The image correction unit 705 uses the same quantizationmethod as that in the first embodiment. That is, the image correctionunit 705 quantizes a 4-bit value Q8 _(—) n nearest to P_k to Pq_k byusing a value Q8 _(—) n in the 8-bit expression as in step S1504. Theimage correction unit 705 then functions as a difference calculationunit and a sum total calculation unit to calculate differences E_jbetween values before and after quantization according to E_j=Pq_k−P_kin step S2005, and updates the sum total E_total of the differences inthe block according to E_total=E_total+E_j in step S2006. In thisembodiment, the block size has 8 pixels. In step S2007, the imagecorrection unit 705 determines whether j=7, that is, the processing iscompleted for all the pixels in the block. If NO in step S2007, theimage correction unit 705 increments k and j by one each to return theprocess to step S2004. If YES in step S2007, the process shifts to acorrection process after step S2008.

In step S2008, the image correction unit 705 determines whether the sumtotal E_total of the differences is larger than 8. If YES in step S2008,the process advances to step S2009 to select a pixel j′ exhibiting themaximum difference among differences E_0 to E_7 in the block, anddecreases a quantized value Pq_k′ of a corresponding pixel number k′ tothe immediately lower quantization level (that is, Q8 _(—) n→Q8_(n−1)).At the same time, the image correction unit 705 sets E_j′=E_j′−17. Inthis embodiment, since the step amount of the quantized value Q8 _(—) nis 17, Pq_k′=Pq_k′−17. In step S2010, the image correction unit 705 thensets the sum total E_total of the differences to E_total=E_total−17. Theprocess then shifts to step S2014.

If NO in step S2008, the process advances to step S2011, in which theimage correction unit 705 determines whether the sum total E_total issmaller than −8. If YES in step S2011, the process advances to stepS2012, in which the image correction unit 705 selects the pixel j′exhibiting the minimum difference among the differences E_0 to E_7 inthe block, and increases the quantized value Pq_k′ of the correspondingpixel number k′ to the immediately higher quantization level (that is,Q8 _(—) n→Q8 _(—) n+1). At the same time, the image correction unit 705sets E_j′=E_j′+17. In this embodiment, since the step amount of thequantized value Q8 _(—) n is 17, Pq_k′=Pq_k′+17.

In step S2013, the image correction unit 705 also sets the sum totalE_total of the differences to E_total=E_total+17. The process thenshifts to step S2014. In step S2104, the image correction unit 705determines whether the value of E_total falls within (+/−) quantizationstep amount/2. That is, the image correction unit 705 determines whether−8≦E_total≦8. If NO in step S2014, the image correction unit 705performs the processing in step S2008 again. If there are a plurality ofpixels exhibiting the maximum or minimum difference in steps S2009 andS2012, the image correction unit 705 may select one of the pixels whichhas the minimum value of j.

If YES in step S2014, the image correction unit 705 determines that theabsolute value of the sum total of the differences converges to anallowable range, and terminates the modifying operation. The processthen advances to step S2015. If NO in step S2011, since −8≦E_total≦8,the process directly advances to step S2015. In step S2015, the imagecorrection unit 705 performs conversion of Q8 _(—) n→Q4 _(—) n as instep S1506 in the first embodiment, and stores the value Q_k afterconversion as an output value in the output image buffer. The imagecorrection unit 705 then completes the processing in the block.Subsequently, the image correction unit 705 determines in step S2016whether the processing is completed for all the pixels within the line.If NO in step S2106, the image correction unit 705 increments the pixelnumber k by one in step S2019. The process advances to step S2003 againto process the next block. If the image correction unit 705 determinesin step S2016 that the processing is completed for all the pixels, theimage correction unit 705 determines in step S2017 whether theprocessing is completed for a predetermined main scanning line (the lastmain scanning line in the page). If NO in step S2017 the imagecorrection unit 705 increments m by one in step S2020. The process thenshifts to step S2002 again. Upon completing the processing for apredetermined number of main scanning lines and determining YES in stepS2020, the CPU 401 terminates the correction amount modification processfor one page.

The manner of performing a series of processing operations in step S2004to S2015 described above will be described with reference to FIG. 20.Assume that as in the first embodiment, the corrected image buffer hasstored values like those indicated by reference numeral 2101 on the lineL_m as a result of an image correction process. First of all, in stepS2004, the image correction unit 705 quantizes the corrected imagesignal P_0=48 to obtain Pq_0=51. In step S2005, difference E_0=3, andthe sum total E_total of the differences is initialized to 0. In stepS2006, therefore, E_total=3. The image correction unit 705 sequentiallyperforms the above processing for P_1 to P_7 in the block to calculatethe quantized signals Pq 0 to Pq 7 indicated by reference numeral 2102and the differences E_1 to E_7 indicated by reference numeral 2103,thereby calculating sum total E_total of differences=28 (2108). When theprocessing for Pq 7 is complete, since j=7, YES is obtained in stepS2007. The process therefore shifts to the next processing in stepS2008.

In step S2008, since E_total=28>8, YES is obtained. The process advancesto step S2009 to select a pixel exhibiting the maximum difference amongE_0 to E_7. In the case shown in FIG. 20, the maximum difference valueamong the differences (2103) is 8. Since there are four pixels E_1, E_2,E_5, and E_6 exhibiting the difference of 8. For this reason, the imagecorrection unit 705 selects E_1 with the minimum pixel number anddecreases the quantization level of Pq_1 corresponding to E_1 by one.That is, the image correction unit 705 converts the value of Pq_1 from187→170. In addition, the image correction unit 705 subtracts 17 fromthe value of E_1 to obtain E_1=−9. Reference numeral 2104 in FIG. 20denotes pixel values after quantization level change; and 2105,differences. The value of a pixel Pq_1 indicated by the hatching asindicated by reference numeral 2104 is a changed pixel. In step S2010,the image correction unit 705 subtracts 17 from sum total E_total ofdifferences=28 to obtain E_total=11 (2109).

In step S2014, the image correction unit 705 determines whether−8≦E_total≦8. Since E_total=11>8, NO is obtained in step S2014. Theprocess shifts to step S2008. In step S2008, YES is obtained. In stepS2009, the image correction unit 705 selects a pixel exhibiting themaximum difference among the differences denoted by reference numeral2105. Since the maximum difference value among the differences (2105) is8 and there are three pixels E_2, E_5, and E_6 exhibiting the differenceof 8, the image correction unit 705 selects E_2 with the minimum pixelnumber, and decreases the quantization level of Pq 2 corresponding toE_2 by one. That is, the image correction unit 705 converts the value ofPq 2 from 187 to 170. In addition, the image correction unit 705subtracts 17 from the value of E_2 to obtain E_2=−9. Reference numeral2106 in FIG. 20 denotes pixel values after quantization level change;and 2107, differences. The value of a pixel Pq 2 indicated by thehatching as indicated by reference numeral 2106 is a changed pixel. Instep S2010, the image correction unit 705 subtracts 17 from sum totalE_total of differences=11 to obtain E_total=−6 (2110). In step S2014,the image correction unit 705 determines whether −8≦E_total≦8, anddetermines “YES”. The image correction unit 705 then terminates themodification process in the block. The process shifts to step S2015. Instep S2015, the image correction unit 705 performs conversion of Q8 _(—)n→Q4 _(—) n as in step S1506 in the first embodiment, and stores thevalue Q_k after conversion as an output value in the output imagebuffer. The image correction unit 705 then completes the processing inthe block. Subsequently, the process shifts to the processing for thenext 8 pixels, and the image correction unit 705 sequentially processesblocks each including 8 pixels.

As described above, in this embodiment, in quantization processing, ifthe sum total of differences is positive, the image correction unit 705changes the quantization level of the value of a pixel, of thedifferences in a block, which is a positive value and exhibits themaximum difference in absolute value to the immediately lower level. Ifthe sum total of the differences is negative, the image correction unit705 changes the quantization level of the value of a pixel, of thedifferences in a block, which is a negative value and exhibits themaximum difference in absolute value to the immediately higher level. Inaddition, the image correction unit 705 repeatedly executes thisquantization processing until the absolute value of the sum total ofdifferences becomes smaller than a predetermined value (eight in thiscase).

As described above, minimizing quantized errors on a block basis caneffectively execute the present invention. Note that in this embodiment,the block length has 8 pixels. However, the number of pixels of a blockis not limited to this. In addition, it is possible to effectivelyexecute the present invention by multiplying the block length and theperiod of halftone processing by integers so as to prevent the period ofcorrection amount modification processing from interfering with theperiod of halftone processing.

Third Embodiment

The first and second embodiments are configured to reduce banding bycorrecting positions. The third embodiment will exemplify a case inwhich banding is reduced by correcting densities (obtaining densitycorrection amounts). This embodiment is the same as the first embodimentin the basic arrangement for correcting an image in synchronism with FGpulses of the motor. For this reason, only correction tables and animage correction process in an image correction unit 705 will bedescribed below.

Examples of correction tables in this embodiment will be described firstwith reference to FIG. 21. Since tables A to D are the same as those inthe first embodiment and FIGS. 11A to 11C, a description of them will beomitted. This embodiment converts a correction value Dc_n in table Dinto a density correction value Dcc_n (table E) according toDcc_n=K′×Dc_n. In this case, K′ is a predetermined coefficient, whichdetermines the correspondence between a density variation ratio [%] anda density correction value. In this case, the density correction valueDcc_n represents a correction amount for a 4-bit (0 to 15) image signalvalue. In the case shown in FIG. 21, K′=0.075. Note that when thedensity variation ratio Dc_n and the density correction value Dcc_n donot have a proportional relationship, it is possible to hold therelationship between density variation ratios Dc_n and the densitycorrection values Dcc_n in the form of a table and to convert Dc_n intoDcc_n by using the table.

As in the case shown in FIG. 12 in the first embodiment, the imagecorrection unit 705 interpolates the density correction value Dcc_n andgenerates the data of a density correction value D_m for each mainscanning line, thereby obtaining table F. The image correction unit 705further computes a density correction value Dq_m by multiplying D_m by17 and rounding off the product to an integer, thereby generating tableG. More specifically, the image correction unit 705 calculates the valueof Dq_m according to Dq_m=floor(D_m×17+0.5). As a value in table G, theimage correction unit 705 obtains the value of q, of p/17 (p=0, 1, . . ., 17), which is nearest to table F. A CPU 401 stores the calculatedinformation of table G in an EEPROM to allow the reuse of theinformation.

<Image Correction Process>

An image correction process in this embodiment will be described nextwith reference to FIG. 22. The image signal processed by a halftoneprocessing unit 704 is temporarily loaded in a line buffer (input imagebuffer) in a RAM 402. Assume that as in the first embodiment, the inputimage buffer in the third embodiment has a size corresponding to onepage.

The input image buffer stores 4-bit pixel values like those indicated by(a) in FIG. 17, which have undergone halftone processing. First of all,in step S2301, the image correction unit 705 sets line number m=0. Inaddition, in this embodiment as well, since exposure for image datastarts at the timing when an FG count value FGs becomes 0, a densitycorrection value for a line L_m is represented by D_m.

In step S2302, the image correction unit 705 initializes the pixelnumber k to 0 in the main scanning direction. In step S2303, the imagecorrection unit 705 converts the density correction value Dq_m into ablock-based correction amount (modified correction amount) by using theconversion table shown in FIG. 23. As described above, densitycorrection value Dq_m=p represents a correction amount of p/17 for a4-bit (0 to 15) input image signal.

If, for example, Dq_m is 1, the image correction unit 705 converts thedata into a 17-pixel block like that denoted by reference numeral 2401.The block 2401 includes one pixel with a correction amount of 1 and 16pixels with a correction amount of 0. Therefore, the average correctionamount in the block is 1/17. A correction amount of 1/17 is expressed ona block basis. Likewise, when Dq_m=2, the block includes two pixels witha correction amount of 1 and 15 pixels with a correction amount of 0,and the average correction amount in the block is 2/17. That is, acorrection amount of 2/17 is expressed on a block basis. The sameapplies to Dq_m=3 to 5. As is obvious from FIG. 23, pixels with acorrection amount of 1 are arranged in each block so as not bedecentered within the block and within the repetition period of blocks.The above conversion allows to perform correction on a 1/17 basis.Assume that the correction amounts converted on a block basis aresequentially represented by D_b k_0 to D_b k_16. Although the abovedescription has exemplified the case in which Dq_m is a positive value,the present invention also assumes that Dq_m is a negative value. WhenDq_m is a negative value, one pixel in the above block is a pixel with acorrection value of −1.

In step S2304, the image correction unit 705 initializes a pixel numberj in a block to 0. In step S2305, the image correction unit 705 adds thecorrection value converted in step S2303 to the input image signalaccording to

I(m,k)=I(m,k)+D _(—) bk _(—) j

According to the above equation, the image correction unit 705sequentially adds a corresponding block-based correction amount D_b k_jto each pixel from the left end of a line m in the input image buffer.

In step S2306, the image correction unit 705 determines whether j=16. IfNO in step S2306, the image correction unit 705 increments k and j byone in step S2309 to perform correction processing again in step S2307.If YES in step S2306, the image correction unit 705 completes thecorrection for the block. In step S2307, the image correction unit 705determines whether the processing is completed for all the pixels withinthe line. If NO in step S2307, the image correction unit 705 incrementsk by one in step S2310, and initializes j to 0 in step S2304. In stepS2305, the image correction unit 705 performs correction processing forthe next block. Upon determining in step S2307 that the processing iscompleted for all the pixels within the line, the image correction unit705 determines in step S2308 whether the processing is completed for apredetermined main scanning line (the last main scanning line in thepage). If NO in step S2308 the image correction unit 705 increments m byone in step S2311 to perform the processing in step S2302 for the nextline. Upon completing the processing for a predetermined number of mainscanning lines and determining “YES” in step S2308, the CPU 401terminates the image correction process for one page.

As has been described above, according to this embodiment, it ispossible to perform correction with 4-bit values (0 to 15) on a 1/17basis, and hence to perform accurate correction.

Other Embodiments

Aspects of the present invention can also be realized by a computer of asystem or apparatus (or devices such as a CPU or MPU) that reads out andexecutes a program recorded on a memory device to perform the functionsof the above-described embodiment(s), and by a method, the steps ofwhich are performed by a computer of a system or apparatus by, forexample, reading out and executing a program recorded on a memory deviceto perform the functions of the above-described embodiment(s). For thispurpose, the program is provided to the computer for example via anetwork or from a recording medium of various types serving as thememory device (for example, computer-readable medium).

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application Nos.2010-282393, filed Dec. 17, 2010 and 2011-256415, filed Nov. 24, 2011,which are hereby incorporated by reference herein in their entirety.

1. An image forming apparatus comprising: a correction amountdetermination unit which determines a correction amount for an imagesignal so as to correct banding as periodic density unevenness in a subscanning direction; an image correction unit which corrects each pixelvalue of an n-bit image signal in accordance with the correction amountdetermined by said correction amount determination unit and outputs theimage signal as a first corrected image signal; and a quantization unitwhich quantizes, for each pixel, the first corrected image signalcorrected by said image correction unit into a second corrected imagesignal of m bits smaller than n bits, wherein said quantization unitdiffuses, in a main scanning direction, quantization errors at the timeof quantization of the first corrected image signal into the secondcorrected image signal so as to cancel the quantization errors within apredetermined region including a plurality of continuous pixels on amain scanning line.
 2. The apparatus according to claim 1, wherein saidquantization unit comprises a difference calculation unit whichcalculates a difference between the second corrected image signal andthe first corrected image signal of a pixel of interest, and an additionunit which adds the difference calculated by said difference calculationunit to the first corrected image signal of a pixel adjacent to thepixel of interest in the main scanning direction.
 3. The apparatusaccording to claim 1, wherein said quantization unit comprises adifferent calculation unit which calculates a difference between thesecond corrected image signal and the first corrected image signal foreach pixel on each main scanning line, a sum total calculation unitwhich calculates a sum total of the differences calculated by saiddifference calculation unit for each predetermined block including aplurality of continuous pixels on a main scanning line, and amodification unit which modifies a second modified image signal in ablock so as to reduce an absolute value of the sum total.
 4. Theapparatus according to claim 3, wherein said modification unit executesquantization processing such that when the sum total is positive, asecond corrected image signal of a pixel having a difference, ofdifferences in a block, which is a positive value and a maximum value inabsolute value is changed to an immediately lower quantization level,and when the sum total is negative, a second corrected image signal of apixel having a difference, of the differences in the block, which is anegative value and a maximum value in absolute value is changed to animmediately higher quantization level, and repeatedly executes thequantization processing so as to reduce the absolute value of the sumtotal to a value smaller than a predetermined value.
 5. The apparatusaccording to claim 1, wherein said correction amount determination unitdetermines, as the correction amount, a position correction amount forshifting an image signal on each main scanning line to an adjacent linein a sub scanning direction.
 6. The apparatus according to claim 5,further comprising an image forming unit which includes a rotationmember and a motor for driving the rotation member and forms an image,and a patch forming unit which forms a patch image for detecting densityunevenness accompanying rotation unevenness of the motor by using saidimage forming unit, wherein said correction amount determination unitcomprises a unit which calculates a difference between an averagedensity of density detection signals from a density sensor which detectsa density of the patch image and a density detection signal obtainedevery time a phase signal associated with driving of the motor isoutput, a unit which calculates a density variation ratio from thedifference at each timing when the phase signal is output, a unit whichcalculates a position correction amount in the sub scanning direction bymultiplying the density variation ratio by a predetermined coefficientat each timing when the phase signal is output, a unit which determinesa position correction amount for each main scanning line byinterpolating the position correction amount between the respectivetimings when the phase signals are output, and a unit which creates atable defining each main scanning line and a determined positioncorrection amount in association with each other and stores the table ina storage unit, and said image correction unit generates the firstcorrected image signal by using the table stored in said storage unit.7. The apparatus according to claim 1, further comprising a halftoneprocessing unit which performs halftone processing for an image signaland outputs the m-bit image signal, wherein said image correction unitconverts each pixel value of an m-bit image signal into an n-bit imagesignal after halftone processing, and then corrects the image signalinto the first corrected image signal.
 8. An image forming apparatuscomprising: a correction amount determination unit which determines acorrection amount for an image signal so as to correct banding asperiodic density unevenness in a sub scanning direction; a quantizationunit which quantizes the correction amount determined by said correctionamount determination unit from n bits to m bits smaller than the n bits;a conversion unit which converts the correction amount quantized by saidquantization unit into a modified correction amount indicating acorrection amount for each block including a plurality of continuouspixels in a main scanning direction; and an image correction unit whichcorrects the image signal by adding a block-based modified correctionamount converted by said conversion unit to a pixel of an m-bit imagesignal which corresponds to the block, wherein said conversion unitperforms conversion such that an average value of block-based modifiedcorrection amounts becomes nearest to a correction amount.
 9. Theapparatus according to claim 8, wherein said conversion unit convertsthe correction amount into the modified correction amount such thatconverted values in the block are not decentered within the block andwithin a repetition period of blocks.
 10. The apparatus according toclaim 8, wherein said correction amount determination unit determines adensity correction amount of an image signal for each main scanning lineas the correction amount.
 11. The apparatus according to claim 1,further comprising a halftone processing unit which performs halftoneprocessing for an image signal and outputs the m-bit image signal,wherein said image correction unit adds the block-based modifiedcorrection amount to a pixel of an m-bit image signal which correspondsto the block after halftone processing.